Two thin lenses have a combined power of $+9 \text{ D}$. When they are separated by a distance of $20 \text{ cm}$,their equivalent power becomes $+\frac{27}{5} \text{ D}$. Their individual powers (in dioptre) are

$A$ concave lens and a convex lens have the same focal length of $20 \ cm$ and are placed in contact. This combination is used to view an object $5 \ cm$ long kept at $20 \ cm$ from the lens combination. As compared to the object,the image will be:

We combined a convex lens of focal length $f_1$ and a concave lens of focal length $f_2$. Their combined focal length is $F$. The combination of these lenses will behave like a concave lens if:

$A$ thin convex lens of focal length $5 \ cm$ and a thin concave lens of focal length $4 \ cm$ are combined together (without any gap) and this combination has magnification $m_1$, when an object is placed $10 \ cm$ before the convex lens. Keeping the positions of the convex lens and object undisturbed, a gap of $1 \ cm$ is introduced between the lenses by moving the concave lens away, which leads to a change in the magnification of the total lens system to $m_2$. The value of $\left|\frac{m_1}{m_2}\right|$ is . . . . . . .

An object is placed $12 \ cm$ to the left of a converging lens of focal length $8 \ cm$. Another converging lens of $6 \ cm$ focal length is placed at a distance of $30 \ cm$ to the right of the first lens. The second lens will produce

$A$ plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. The lenses are made of different materials with refractive indices $n_1$ and $n_2$,and $R$ is the radius of curvature of the curved surfaces. What is the focal length of the combination?